This paper is concerned with the generalized Allen-Cahn equation with a nonlinear mobility that can degenerate, which also includes an advection term as found in phase-field models. A class of maximum principle preserving schemes will be studied for the generalized Allen-Cahn equation, with either the commonly used polynomial free energy or the logarithmic free energy, and with a nonlinear dege...

The generalized local maximum principle for a difference operator L» asserts that if Lam(jc) > 0 then Vu cannot attain its positive maximum at the net-point x. Here r is a local net-operator such that Tu = u + 0(/i) for any smooth function u. This principle, with simple forms of V, is proved for some quite general classes of second-order elliptic operators Lh, whose associated global matrices a...

Economic disruptions (techonological change, trade liberalization, immigration flows) generally create winners and losers, i.e., wage gains for some individuals losses others. The compensation problem consists of designing a reform the existing income tax system that offsets wefare by redistributing winners. We derive closed-form formula compensating its impact on government budget when only di...

The possibility of reconciliation between canonical probability distributions obtained from the q-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is investigated into. Canonical probability distributions are constrained by both: (i) the additive duality of generalized statistics and (ii) normal averages expectatio...

We discuss the proof of a version of the maximum principle with state space constraints for data with very weak regularity properties, using the classical method of packets of needle variations (PNVs), as in Pontryagin’s book, but coupling it with a nonclassical theory of multivalued differentials, the so-called “generalized differential quotients” (GDQs). The key technical point of our argumen...

We describe a speedup for training conditional maximum entropy models. The algorithm is a simple variation on Generalized Iterative Scaling, but converges roughly an order of magnitude faster, depending on the number of constraints, and the way speed is measured. Rather than attempting to train all model parameters simultaneously, the algorithm trains them sequentially. The algorithm is easy to...